Suppose that there are 1200 units of a nonrenewable resource available over two periods (0 and 1). Demand in each period is given by P = 2000 - Q. Marginal cost is a constant 400 in both periods. The discount rate is 10 percent.

1. What is the dynamically efficient allocation of the 1200 units of the nonrenewable resource?Please show your work.
2. What will be the prices in each of the two periods? Please show your work.
3. Calculate the rate of royalty increase.Does Hotelling'srule hold?
4. Calculate the rate of price increase.

2. Suppose that the basic setup of the problem above were the same, except that now the discount rate rises to 20 percent.

1. Re-compute the dynamically efficient allocation of the 1200 units of the nonrenewable resource. Please show your work.
2. What will be the prices in each of the two time periods? Show your work.

3. Correctly draw the price paths for questions 1 and 2 above in a single fully-labeled diagram below. (ii) Provide a brief economic explanation for why the two price paths have different slopes.